A channel flows from north to south at a rate of $15$ mph. A sailboat heads at an angle of $30º$ upstream at a rate of $40$ mph. A strong wind blows directly northwest at a rate of $30$ mph.

1. Write each of the vectors in component form.

   Step (a):

   sailboat: $⟨40\cos(30°), 40\sin(30°)⟩$

2. What is the resultant vector in component form?

   Hint (b):

   Add the three vectors from part (a). This vector is a rate, or miles per hour, vector.

3. What will the sailboat’s true course and speed be?

   Hint (c):

   What are the magnitude and direction of the vector in part (b)?

4. If the channel is $20$ miles wide, how long will it take to cross the channel?

   Hint (d):

   Only the horizontal component of the resultant vector needs to be used to solve this problem.

5. How far north from its starting position will the sailboat exit the channel?

   Hint (e):

   Use the vertical component of the resultant vector from part (b) and the time from part (e) to solve this problem.